Christianity turning point in Rome from forbidden became the center of Christianity

Ron I have a question to ask about church history. From which I knew, Rome is very hate or forbid every Christianity at that times(Peter's times). What is the turning point for Rome which before they forbid Christianity but now Rome (Vatican) became the center of all Christianity? Is there any Rome's king who are Christian and is that king is the turning point for Christianity in Rome?

In 313, when Constantine obtained sufficient power in the Roman empire, he proclaimed a policy of toleration of Christianity in the empire. Previously, Christians were severely persecuted.http://www.newadvent.org/cathen/04295c.htm

In 325, Constantine became the sole emperor of the Roman empire.

In 337, he died shortly after receiving baptism as a Christian.

"Constantine can rightfully claim the title of Great, for he turned the history of the world into a new course and made Christianity, which until then had suffered bloody persecution, the religion of the State."